Best Known (40−21, 40, s)-Nets in Base 16
(40−21, 40, 103)-Net over F16 — Constructive and digital
Digital (19, 40, 103)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (3, 13, 38)-net over F16, using
- net from sequence [i] based on digital (3, 37)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 3 and N(F) ≥ 38, using
- net from sequence [i] based on digital (3, 37)-sequence over F16, using
- digital (6, 27, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- digital (3, 13, 38)-net over F16, using
(40−21, 40, 149)-Net over F16 — Digital
Digital (19, 40, 149)-net over F16, using
(40−21, 40, 150)-Net in Base 16 — Constructive
(19, 40, 150)-net in base 16, using
- 2 times m-reduction [i] based on (19, 42, 150)-net in base 16, using
- base change [i] based on digital (1, 24, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- base change [i] based on digital (1, 24, 150)-net over F128, using
(40−21, 40, 14990)-Net in Base 16 — Upper bound on s
There is no (19, 40, 14991)-net in base 16, because
- 1 times m-reduction [i] would yield (19, 39, 14991)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 91401 221820 527983 782475 275060 313505 204140 049401 > 1639 [i]